The Number of Negative Entries in a Sign Pattern Allowing Orthogonality

Abstract.

A ± sign pattern is a matrix whose entries are in the set {+,−}. An n×n ± sign pattern A allows orthogonality if there exists a real orthogonal matrix B in the qualitative class of A. In this paper, we prove that for n≥3 there is an n×n ± sign pattern A allowing orthogonality with exactly k negative entries if and only if n−1≤k≤n²−n+1.